Soliton molecules, multi-breathers and dynamical behaviors of the Lakshmanan–Porsezian–Daniel equation

Zuoxin Xiong, Bo Ren, Wanli Wang

Research output: Contribution to journalArticlepeer-review


In this work, we investigate the Lakshmanan–Porsezian–Daniel (LPD) equation with high-order nonlinear and dispersion terms which can describe an inhomogeneous one-dimensional anisotropic Heisenberg ferromagnetic spin chain and alpha helical protein. With the aid of auxiliary function, the bilinear form of the LPD equation is constructed. Multi-soliton solutions are obtained by solving the corresponding bilinear form. Multi-breather solutions are presented by assuming the complex conjugation relations on the parameters of the multi-solitons. The dynamics of one breather, two breathers and their interactions are constructed by selecting the appropriate parameters. The strength of the high-order nonlinear and dispersion effects plays a key role in the breather solutions. Soliton molecule, the breather–soliton molecule and the breather molecule are discovered by applying the velocity resonance conditions. The interactions among the soliton molecules, which could be observed in marine and oceanic waters, are investigated through numerical simulation.

Original languageEnglish
Article number1051
JournalEuropean Physical Journal Plus
Issue number11
StatePublished - Nov 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.


This work is supported by the National Natural Science Foundation of China Grant Nos. 12375006, 11975156, 12105243 and 11775146. The authors are in debt to thank Dr. Xin-Wei Jin for his help to offer the numerical simulation on the stability of the soliton molecule.

FundersFunder number
National Natural Science Foundation of China11975156, 12105243, 11775146, 12375006


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